scholarly journals Maximum principle for the generalized time-fractional diffusion equation

2009 ◽  
Vol 351 (1) ◽  
pp. 218-223 ◽  
Author(s):  
Yury Luchko
Keyword(s):  
Maximum Principle ◽  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Time Fractional Diffusion Equation ◽  
Generalized Time

scholarly journals Solving Fractional Diffusion Equation via the Collocation Method Based on Fractional Legendre Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Muhammed Syam ◽  
Mohammed Al-Refai
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Collocation Method ◽  
Path Following ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Legendre Functions ◽  
Time Fractional Diffusion Equation ◽  
Path Following Methods ◽  
Generalized Time

A formulation of the fractional Legendre functions is constructed to solve the generalized time-fractional diffusion equation. The fractional derivative is described in the Caputo sense. The method is based on the collection Legendre and path following methods. Analysis for the presented method is given and numerical results are presented.

scholarly journals On the maximum principle for a time-fractional diffusion equation

2017 ◽  
Vol 20 (5) ◽  
Author(s):  
Yuri Luchko ◽  
Masahiro Yamamoto
Keyword(s):  
Maximum Principle ◽  
Diffusion Equation ◽  
Time Derivative ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
The Maximum Principle ◽  
Time Fractional Diffusion Equation

AbstractIn this paper, we discuss the maximum principle for a time-fractional diffusion equationwith the Caputo time-derivative of the order

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